JEE Advanced Mock Test - 2 (Paper II) - JEE MCQ

Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle.

Assume that the sound of the whistle is composed of components varying in frequency from f₁ = 800 Hz to f₂ = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.

The spread of frequency as observed by the passengers in train B is

A resistance of 2Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s^-2).

The magnitude of the normal reaction that acts on the block at the point Q is

Work function of metal A is equal to the ionization energy of hydrogen atom in first excited state. Work function of metal B is equal to the ionization energy of He+ ion in second orbit. Photons of same energy E are incident on both A and B. Maximum kinetic energy of photoelectrons emitted from A is twice that of photoelectrons emitted from B.

Value of E ( in eV) is

When you throw a ball in air with some velocity at some angle with horizontal, vertical component of velocity at highest point is zero and horizontal component of velocity remains unchanged.

Velocity of a projectile at height 15 m from ground is Here, is in horizontal direction and vertically upwards. Then

Angle of projectile with ground is

A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

1 kg of ₁H² is used in fusion reactor to produce electric power.
The nuclear reaction is ₁H² + ₁H² → ₂He⁴
It is given that mass of ₁H² is 2.0141 u and mass of ₂He⁴ is 4.0026 u
The energy liberated is  P × 10¹⁴ J
To convert this nuclear energy into electrical energy. The water at 300 K is heated to convert into steam at temperature 800 K. The left over steam is at 400 K. The energy supplied to electric grid is  Q × 10¹⁴ J.
Specific heat capacity of water = 4.2 × 10³ J/kg^-k,
Specific heat capacity of steam = 2 × 10³ J/kg^-k,
Latent heat of vaporization of water = 2.25 × 10⁶ J/kg
1amu = 931MeV/c²  

Find the value of P. 

1 kg of ₁H² is used in fusion reactor to produce electric power.
The nuclear reaction is ₁H² + ₁H² → ₂He⁴
It is given that mass of ₁H² is 2.0141 u and mass of ₂He⁴ is 4.0026 u
The energy liberated is  P × 10¹⁴ J
To convert this nuclear energy into electrical energy. The water at 300 K is heated to convert into steam at temperature 800 K. The left over steam is at 400 K. The energy supplied to electric grid is  Q × 10¹⁴ J.
Specific heat capacity of water = 4.2 × 10³ J/kg^-k,
Specific heat capacity of steam = 2 × 10³ J/kg^-k,
Latent heat of vaporization of water = 2.25 × 10⁶ J/kg
1amu = 931MeV/c²  

Find the value of Q. 

A solid cylinder and hemisphere are joined as shown in the figure. Combined mass of the cylinder and the hemisphere is 1/3kg. The cylinder is painted shiny white and the hemisphere is painted dark black. The initial temperature of the body is T_i = 300 K and it is released form rest in gravity free space where the temperature of surrounding is 0K. The body attains terminal velocity v₀. Its specific heat capacity (S) is given in the shown graph.

Find the total energy (in KJ) radiated by the body.

A solid cylinder and hemisphere are joined as shown in the figure. Combined mass of the cylinder and the hemisphere is 1/3kg. The cylinder is painted shiny white and the hemisphere is painted dark black. The initial temperature of the body is T_i = 300 K and it is released form rest in gravity free space where the temperature of surrounding is 0K. The body attains terminal velocity v₀. Its specific heat capacity (S) is given in the shown graph.

Find the terminal velocity v₀ (in mm/s) of the body.

A.DC circuit consisting of two cells of emf V and 2V having no internal resistance are connected with two capacitors of capacity C and 2C and four resistors R, R, 2R and 2R as shown in figure. The ammeter and voltmeter used in the circuit are ideal.

The reading of the ammeter as soon as the switch is closed is

An ideal diatomic gas is expanded so that the amount of heat transferred to the gas is equal to the decrease in its internal energy.

The molar specific heat of the gas in this process is given by C whose value is

Which of the following statements are correct?

If total entropy change during steps-1,3 and 5 be ’x’ J/K, then the value of  is .....

If during step-5, the system exchanges heat from a reserv oir at temperature ‘T₅ K’, then value of T₁/T₂ is:

The ratio of the molar mass of ‘X’ to the total number of ozonides that ‘X’ can form, is…….

In the compounds, X, Y, Z, A, B and C.
If the sum of the number of pi-bonds in all of the above product = m and if degree of unsaturation of (C) be n, then find the value of 2m/n.

If a·b·c = 0, then angle between the lines is q, then 1/2 tan²θ is

Total number of ordered triplets (a, b, c) are

The number of points P on ellipse is three, when the area of the , then the 
value of  is equal to 

The number of point P on ellipse is one, when the area of  then the v alue of  is equal to

A circular disc is allowed to roll on the surface of a rough horizontal fixed cylinder of radius R = /20 m. The centres of the cylinder and the disc are connected by a massless rgid rod. The ends of the massless rigid rod are hinged at the centre of the disc and centre of the cylinder so that the disc can roll over the outer surface of the cylinder without slipping at any point during motion. The disc is released from rest from the top of the cylinder as shown in the figure. Radius of the disc is r = 3/20 m.

Hinged points are v ery smooth so that no loss of energy takes place. Consider the situation when the rod becomes horizontal the magnitude of acceleration of point A (which is on the disc and is in contact with the cylinder) is a_A and speed of point B is v_B. Then choose the correct option. (take g = 10 m/s²)

An inclined plane ABCD is shown in the figure. It is inclined at an angle of 45° from horizontal. A block is placed on the inclined plane. The plane is accelerating along x-axis with an acceleration, a = 5 m/s². The minimum value of coefficient of friction between the block and the plane required, so that the block does not slip on the plane, is (g = 10 m/s²)

Which of the following is an example of a redox reaction?

A disaccharide does NOT give a positive test for Tollen’s reagent. Upon acidic hydrolysis, it gives an equimolar mixture of two different monosaccharides, both of which can be oxidized by bromine water. The correct structure of disaccharide is:

Let F : R → R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x ∈ (1/2, 3). Let f(x) = xF(x) for all x ∈ R.
if  then which of the following expressions is correct?

Consider the following function:
, where k is a positive integer.
Which of the following statements are true?